What is a Hohmann transfer orbit?
A Hohmann transfer is the lowest-energy two-impulse maneuver between two coplanar circular orbits. It rides an elliptical transfer orbit tangent to both circles: a first burn Δv₁ raises the spacecraft from the inner circle onto the ellipse, and a second burn Δv₂ half an orbit later circularizes it at the target radius.
Why it is fuel-optimal
For radius ratios up to about 11.94, the Hohmann transfer needs the least total Δv of any two-impulse coplanar transfer, which is why it is the workhorse for LEO-to-GEO orbit raising and interplanetary departures. Above that ratio a three-burn bi-elliptic transfer can need slightly less fuel, at the cost of a far longer flight.
How to use the simulator
Enter the departure radius r₁ and target radius r₂. Each burn is found from the vis-viva equation v = √(μ(2/r − 1/a)), and the transfer time is half the period of the transfer ellipse, t = π√(a³/μ) with a = (r₁+r₂)/2 (Kepler's third law). The readout shows both burns, the total Δv and the coast time while the ellipse animates.
Note: distances and the gravitational parameter μ = GM are shown in the units of the chosen central body. The model is an idealized two-body, coplanar, instantaneous-burn approximation — real missions add plane changes, finite-burn losses and third-body perturbations.
Frequently asked questions
What is the delta-v of a Hohmann transfer?
It is the sum of two burns from the vis-viva equation v = sqrt(mu*(2/r - 1/a)): the first at the inner radius to enter the transfer ellipse, the second at the outer radius to circularize. The tool reports each burn and the total.
How long does a Hohmann transfer take?
Exactly half the period of the transfer ellipse, t = pi*sqrt(a^3/mu) with a = (r1 + r2)/2. A LEO-to-GEO transfer takes about 5 hours; an Earth-to-Mars Hohmann transfer takes about 259 days.
When is a Hohmann transfer not optimal?
When the ratio of final to initial radius is greater than about 11.94, a three-burn bi-elliptic transfer needs less total delta-v, trading a small fuel saving for a much longer transfer time.
Does a Hohmann transfer handle plane changes?
No. It assumes both orbits lie in the same plane. An inclination change needs an extra out-of-plane burn, which is often combined with the apoapsis burn to reduce the total cost.